There are a few key things that you’d notice between high quality and very low quality audio. Mostly, a loss of information, which would result in a muffled audio, a lack of crispy sounds and a loss of general clarity, as well as unpleasant distortion and other made-up noise at worst.

For 99.9% of people, it’s not really an mp3 vs wav/aiff comparison, but rather a kbps comparison. High quality mp3 (320kbps) is usually indistinguishable from lossless formats for most people.

For a good reasonable idea, compare 128kbps vs 320kbps at the bottom of this page and pay attention to the cymbals and other high-pitched sounds. You should notice that 128kbps sounds a bit more opaque, like it loses a lot of its spark, whereas 320 sounds crisp and clearer.

That being said, it’s not a huge difference unless you go below 128, and there’s no point in listening to wav and lossless files if you use Bluetooth, since Bluetooth hard-caps all your rates at 320kbps anyway. But I think it’s fairly noticeable anyway.